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Mathematical properties of Klein-Gordon-Boussinesq systems
A. Durán, A. Esfahani, G. Muslu
The Klein-Gordon-Boussinesq (KGB) system is proposed in the literature as a model problem to study the validity of approximations in the long wave limit provided by simpler equatio…
Multi-solitons of one-dimensional Boussinesq equation
Vicente Alvarez, Amin Esfahani
The existence of multi-speed solitary waves for the one-dimensional good Boussinesq equation with a power nonlinearity is proven. These solutions are shown to behave at large times…
The Cauchy problem for the nonlinear Schrödinger equation with a convolution potential
Amin Esfahani, Achenef Tesfahun
This paper investigates the nonlinear Schrödinger equation with a singular convolution potential. It demonstrates the local well-posedness of this equation in a modified Sobolev sp…
Well-posedness and analyticity of solutions for the sixth-order Boussinesq equation
Amin Esfahani, Achenef Tesfahun
Studied in this paper is the sixth-order Boussinesq equation. We extend the local well-posedness theory for this equation with quadratic and cubic nonlinearities to the high dimens…